I had the impression that the climb's location in the stage (early on, towards the end after additional climbs, etc) also influenced the category. Is this not true?

Absolutely not.
The categories are the rating of how difficult the climb is. You can have a stage with Cat 1 out the gate, followed by a Cat 4, and back to a Cat 1 again. Nothing to do with the order in which they are in the stage

Absolutely not.
The categories are the rating of how difficult the climb is. You can have a stage with Cat 1 out the gate, followed by a Cat 4, and back to a Cat 1 again. Nothing to do with the order in which they are in the stage

What I have always heard is there is no system but that later climbs often get bigger numbers then a similar climb at the beginning of the stage.

Absolutely not.
The categories are the rating of how difficult the climb is. You can have a stage with Cat 1 out the gate, followed by a Cat 4, and back to a Cat 1 again. Nothing to do with the order in which they are in the stage

Absolutely not.
The categories are the rating of how difficult the climb is. You can have a stage with Cat 1 out the gate, followed by a Cat 4, and back to a Cat 1 again. Nothing to do with the order in which they are in the stage

I wouldn't say "absolutely not" True you can have a Cat 1 at the beginning of a stage and a 4 at the end.

However, whether a climb is considered an Cat 1, or an HC climb can be influenced by where it is on a stage. A climb that in the middle of a stage might get labeled a 1, may well be labeled HC if its a mountain top finish, particularly if there are no other HC climbs on the stage.

Just look at Friday's profile. The last climb at 10k average 7% is a bit light as HC climbs go, but its labeled HC for friday's race.

You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.